Details

Time bar (total: 4.5m)

sample290.0ms

Algorithm
intervals
Results
60.0ms161×body80valid
57.0ms37×body640valid
49.0ms332×body80nan
23.0ms27×body1280valid
14.0ms17×body1280nan
14.0ms22×body640nan
8.0ms18×body320valid
4.0ms13×body160valid
3.0ms8×body320nan
1.0ms5×body160nan

simplify365.0ms

Calls
1 calls:
Slowest
364.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.6b

localize46.0ms

Local error

Found 4 expressions with local error:

20.4b
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
13.6b
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
0.4b
(* (sqrt 2) t)
0.0b
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))

rewrite3.4s

Algorithm
rewrite-expression-head
Rules
1110×add-sqr-sqrt
504×sqrt-prod
495×times-frac
301×unswap-sqr
298×*-un-lft-identity
285×difference-of-squares
238×associate-*l*
146×add-cube-cbrt
84×*-commutative
81×associate-*r*
76×distribute-lft-out--
57×swap-sqr
25×associate-/r*
16×associate-/l*
11×add-cbrt-cube add-exp-log
7×pow1
6×add-log-exp
4×sqrt-div associate--l+ insert-posit16
3×flip3-- flip--
2×distribute-rgt-in cbrt-undiv +-commutative distribute-lft-in div-exp prod-exp associate-/r/ cbrt-unprod
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log pow-prod-down div-inv
Calls
4 calls:
Slowest
1.3s
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
1.1s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
993.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
11.0ms
(* (sqrt 2) t)

series2.3s

Calls
4 calls:
Slowest
1.4s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
509.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
282.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
63.0ms
(* (sqrt 2) t)

simplify2.9m

Calls
935 calls:
Slowest
741.0ms
(/ (* (sqrt (sqrt 2)) (sqrt t)) (sqrt (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))))
710.0ms
(/ (* (sqrt (cbrt 2)) t) (sqrt (- (sqrt (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t))))) l)))
667.0ms
(/ (sqrt (* (sqrt 2) t)) (sqrt (- (sqrt (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t))))) (* (sqrt l) (sqrt l)))))
663.0ms
(/ (* (sqrt (sqrt 2)) t) (sqrt (- (sqrt (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t))))) (* (sqrt l) (sqrt l)))))
639.0ms
(/ (sqrt t) (sqrt (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))))

prune8.8s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 3.9b

localize28.0ms

Local error

Found 4 expressions with local error:

27.0b
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
1.4b
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
0.4b
(* (sqrt 2) t)
0.1b
(* (* l 2) (/ l x))

rewrite617.0ms

Algorithm
rewrite-expression-head
Rules
89×associate-*r/
69×*-un-lft-identity
57×associate-*l*
47×add-sqr-sqrt
44×frac-add
28×add-cube-cbrt
24×flip3-+ sqrt-div flip-+
20×associate-/l*
19×associate-*r*
18×add-cbrt-cube add-exp-log distribute-lft-out
16×sqrt-prod
15×associate-/r*
12×pow1
11×times-frac
10×clear-num un-div-inv
9×unswap-sqr
7×prod-exp cbrt-unprod
6×add-log-exp
5×frac-2neg
4×associate-+l+ pow-prod-down insert-posit16
3×+-commutative *-commutative
2×distribute-rgt-in cbrt-undiv distribute-lft-in div-exp
1×rem-sqrt-square sum-log sqrt-pow1 pow1/2 div-inv
Calls
4 calls:
Slowest
311.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
273.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
22.0ms
(* (* l 2) (/ l x))
7.0ms
(* (sqrt 2) t)

series426.0ms

Calls
4 calls:
Slowest
218.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x))))
111.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
54.0ms
(* (sqrt 2) t)
43.0ms
(* (* l 2) (/ l x))

simplify19.5s

Calls
170 calls:
Slowest
545.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l 2) (/ l x)))
439.0ms
(- (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))
391.0ms
(- (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))) (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))))
361.0ms
(sqrt (+ (* (* (* t t) (+ (pow (/ 4 x) 3) (pow 2 3))) (/ x (cbrt l))) (* (+ (* (/ 4 x) (/ 4 x)) (- (* 2 2) (* (/ 4 x) 2))) (* (* l 2) (* (cbrt l) (cbrt l))))))
353.0ms
(+ (* (* (* t t) (+ (pow (/ 4 x) 3) (pow 2 3))) (cbrt x)) (* (+ (* (/ 4 x) (/ 4 x)) (- (* 2 2) (* (/ 4 x) 2))) (* (* l 2) (/ l (* (cbrt x) (cbrt x))))))

prune2.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.7b

localize65.0ms

Local error

Found 4 expressions with local error:

27.0b
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l (sqrt 2)) (* (sqrt 2) (/ l x)))))
1.4b
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l (sqrt 2)) (* (sqrt 2) (/ l x))))
0.4b
(* (sqrt 2) t)
0.4b
(* l (sqrt 2))

rewrite734.0ms

Algorithm
rewrite-expression-head
Rules
124×associate-*r/
59×*-un-lft-identity
45×associate-*l*
44×frac-add
28×add-sqr-sqrt
24×flip3-+ sqrt-div flip-+
20×sqrt-prod
19×add-cube-cbrt
18×distribute-lft-out
16×associate-/l*
12×associate-/r*
9×pow1 associate-*r*
8×clear-num add-cbrt-cube add-exp-log un-div-inv
6×add-log-exp
4×associate-+l+ frac-2neg insert-posit16 unswap-sqr
3×+-commutative
2×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp *-commutative cbrt-unprod
1×rem-sqrt-square sum-log sqrt-pow1 pow1/2
Calls
4 calls:
Slowest
409.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l (sqrt 2)) (* (sqrt 2) (/ l x)))))
290.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l (sqrt 2)) (* (sqrt 2) (/ l x))))
14.0ms
(* l (sqrt 2))
14.0ms
(* (sqrt 2) t)

series572.0ms

Calls
4 calls:
Slowest
317.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l (sqrt 2)) (* (sqrt 2) (/ l x)))))
156.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l (sqrt 2)) (* (sqrt 2) (/ l x))))
50.0ms
(* l (sqrt 2))
49.0ms
(* (sqrt 2) t)

simplify19.8s

Calls
137 calls:
Slowest
432.0ms
(- (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))
381.0ms
(sqrt (+ (pow (* (* t t) (+ (/ 4 x) 2)) 3) (pow (* (* l (sqrt 2)) (* (sqrt 2) (/ l x))) 3)))
374.0ms
(sqrt (- (* (* (* t t) (+ (/ 4 x) 2)) (* (* t t) (+ (/ 4 x) 2))) (* (* (* l (sqrt 2)) (* (sqrt 2) (/ l x))) (* (* l (sqrt 2)) (* (sqrt 2) (/ l x))))))
361.0ms
(+ (* (* (* t t) (+ (pow (/ 4 x) 3) (pow 2 3))) (cbrt x)) (* (+ (* (/ 4 x) (/ 4 x)) (- (* 2 2) (* (/ 4 x) 2))) (* (* l (sqrt 2)) (* (sqrt 2) (/ l (* (cbrt x) (cbrt x)))))))
343.0ms
(sqrt (+ (* (* (* t t) (+ (pow (/ 4 x) 3) (pow 2 3))) (cbrt x)) (* (+ (* (/ 4 x) (/ 4 x)) (- (* 2 2) (* (/ 4 x) 2))) (* (* l (sqrt 2)) (* (sqrt 2) (/ l (* (cbrt x) (cbrt x))))))))

prune2.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.7b

localize50.0ms

Local error

Found 4 expressions with local error:

27.0b
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l (sqrt 2)) (* (sqrt 2) (/ l x)))))
1.4b
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l (sqrt 2)) (* (sqrt 2) (/ l x))))
0.4b
(* l (sqrt 2))
0.3b
(* (sqrt 2) (/ l x))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
133×associate-*r/
68×*-un-lft-identity
45×associate-*l*
44×frac-add
42×add-sqr-sqrt
27×add-cube-cbrt
24×flip3-+ sqrt-div flip-+
21×sqrt-prod
20×associate-/l*
19×associate-*r*
18×distribute-lft-out
15×associate-/r*
11×times-frac add-cbrt-cube add-exp-log
10×clear-num un-div-inv
9×pow1
6×add-log-exp unswap-sqr
5×frac-2neg
4×associate-+l+ insert-posit16
3×+-commutative prod-exp cbrt-unprod
2×distribute-rgt-in distribute-lft-in pow-prod-down *-commutative
1×cbrt-undiv rem-sqrt-square sum-log sqrt-pow1 pow1/2 div-exp div-inv
Calls
4 calls:
Slowest
840.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l (sqrt 2)) (* (sqrt 2) (/ l x)))))
359.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l (sqrt 2)) (* (sqrt 2) (/ l x))))
12.0ms
(* (sqrt 2) (/ l x))
10.0ms
(* l (sqrt 2))

series636.0ms

Calls
4 calls:
Slowest
345.0ms
(sqrt (+ (* (* t t) (+ (/ 4 x) 2)) (* (* l (sqrt 2)) (* (sqrt 2) (/ l x)))))
153.0ms
(+ (* (* t t) (+ (/ 4 x) 2)) (* (* l (sqrt 2)) (* (sqrt 2) (/ l x))))
79.0ms
(* (sqrt 2) (/ l x))
59.0ms
(* l (sqrt 2))

simplify20.6s

Calls
163 calls:
Slowest
534.0ms
(- (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))
381.0ms
(sqrt (+ (* (* (* t t) (+ (pow (/ 4 x) 3) (pow 2 3))) (cbrt x)) (* (+ (* (/ 4 x) (/ 4 x)) (- (* 2 2) (* (/ 4 x) 2))) (* (* l (sqrt 2)) (* (sqrt 2) (/ l (* (cbrt x) (cbrt x))))))))
369.0ms
(sqrt (+ (pow (* (* t t) (+ (/ 4 x) 2)) 3) (pow (* (* l (sqrt 2)) (* (sqrt 2) (/ l x))) 3)))
362.0ms
(- (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))) (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))))
354.0ms
(+ (* (* (* t t) (+ (pow (/ 4 x) 3) (pow 2 3))) (- x)) (* (+ (* (/ 4 x) (/ 4 x)) (- (* 2 2) (* (/ 4 x) 2))) (* (* l (sqrt 2)) (* (sqrt 2) (- l)))))

prune2.7s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.7b

regimes1.2s

Accuracy

68% (8.6b remaining)

Error of 9.5b against oracle of 0.9b and baseline of 27.8b

bsearch283.0ms

end0.0ms

sample8.4s

Algorithm
intervals
Results
3.0s9884×body80nan
1.0s5111×body80valid
983.0ms1035×body640valid
951.0ms851×body1280valid
608.0ms546×body1280nan
546.0ms635×body640nan
446.0ms658×body320valid
201.0ms328×body320nan
149.0ms345×body160valid
148.0ms202×body160nan